Charge, atomic distribution

Let us now consider some general aspects of the atomic charge distributions. For the H atoms, the calculated natural atomic charges Qw are found to depend most strongly on whether the atom appears at a bridging H(p), terminal H(t), or BH2 extra H(x) position. Typical Ou values fall within the disjoint ranges... 

Table 3.40. Boron atomic charge distributions in boron hydrides see Fig. 3.103 for atom numberings), comparing Lipscomb s zeroth-order ZO) estimates note 154) with NPA atomic charges...

The spherical harmonic density functions are referred to as multipoles, since the functions with 1 = 0, 1, 2, 3, 4, etc., correspond to components of the charge distribution p r) which give nonzero contributions to the monopole (/ = 0), dipole (/ = 1), quadrupole (/ = 2), octupole (/ = 3), hexadecapole (/ = 4), etc., moments of the atomic charge distribution. 

Seiler and Dunitz point out that the main reason for the widespread acceptance of the simple ionic model in chemistry and solid-state physics is its ease of application and its remarkable success in calculating cohesive energies of many types of crystals (see chapter 9). They conclude that the fact that it is easier to calculate many properties of solids with integral charges than with atomic charge distributions makes the ionic model more convenient, but it does not necessarily make it correct. 

A crude estimation of the charge-density distribution on simple metal surfaces can be made by assuming that the electron charge for each atom is spherical. Especially, as shown by Cabrera and Goodman (1972), by representing the atomic charge distribution with a Yukawa function. 

If the atomic charge distributions are assumed to be spherically symmetric, the effective inverse distance y is computed as... 

Marchi and co-workers [27,28] have applied Equation (1.79) in the context of classical MD by using a Fourier pseudo-spectral approximation of the polarization vector field. This approach provides a convenient way to evaluate the required integrals over all volume at the price of introducing in the extended Lagrangian a set of polarization field variables all with the same fictitious mass. They also recognized the cmcial requirement that both the atomic charge distribution and the position-dependent dielectric constant be continuous functions of the atomic positions and they devised suitable expressions for both. 

By the MEM charge density studies, the different features of encapsulated metal atoms in C82 were revealed for La C82 [2] and Sc C82 [3]. To compare the three-dimensional shape of the metal-atom charge distribution, a section of the equi-density surface of a La C82 molecule is presented in Fig. 9 together with the result for Sc C82 (Isomer I). The equi-density level is 1.8 e/A3. The number of electrons belonging to the Sc atom of Sc C82 was 18.8(2) e, which is close to the 19.0 e of a divalent state of the scandium atom, Sc2+. This indicates that the Sc C82 (I) is an endohedral metallofullerene whose formal electronic structure is Sc2+C82. This result has brought the long discussion as to whether the Sc atom is in a divalent or trivalent state inside the carbon cage [26-29] to an end experimentally. 

Not only is hybridization an artificial simulation without scientific foundation, but even the assumed "orbital shapes" that it relies upon, are gross distortions of actual electron density distributions. The density plot shown above, like all textbook caricatures of atomic orbitals, is a misrepresentation of the spherical surface harmonics that describe normal excitation modes of atomic charge distributions. These functions are defined in the surface of the charge-density function, as in Fig. 2.13, and not at r = 0, as shown in Figure 2.16. 

Figure 17. Atomic charge distribution of selected compounds (e 1(F) (26, 27, 28J...

Qik - Qi,-kV for k > 0, where the subscripts c and s allude to the trigonometric functions associated with complex algebra). Some of these components will be zero if the atomic charge distribution has elements of symmetry. This can be deduced as described earlier, though each atomic site usually has less symmetry, and thus more nonzero multipoles, than the entire molecule. 

The 2D RDF shows a distance axis and a property axis showing the partial atomic charge distribution. Since the probability-weight fnnction p is omitted, the fnnction simply splits into distance space and property space. The distance axis is equivalent to a one-dimensional RDF, whereas the property axis shows the charge distribution at a certain distance. The two intense peaks represent the C-H and C-H ... 

Diaryltetrazole-5-thiones were prepared and theoretical studies on atomic charge distributions were performed on these compounds <05JOC8322>. 

Figure 16. Net atomic charge distribution for the benzyl carbanion. The top two figures are for the metal complex, (NHs)2LiCH2C6H5, and indicate a net charge on the organic group of about —0.5 electron. The bottom two figures are for the isolated benzyl carbanion (83).

CNDO/INDO estimates of the net atomic charge distribution for the benzyl and fluorenyl carbanions are given in Figures 16 and 17 (25). The electrostatic potential energy distribution at 2.0 A above the mean plane for these distributions of point charges are shown in Figures 18 and 19. The electrostatic model predicts that the lithium atom would be located over the potential energy minima in the two carbanions— that is, on a normal to the fluorenyl plane that intersects the plane just inside the 9 position, and a normal to the mean benzylic plane that intersects the plane about 0.4 A for C(7) on the C(l)—C(7) bond. In fact, the observed position of the lithium atom is about 1.5 A from the pre-... 

Figure 18. Potential energy surface at 2.0 A above the plane of the fluorenyl carbanion calculated from the CNDO II atomic charge distribution of Figure 17. Contour lines are drawn at levels of 0.02 eV (83).

An atomic charge distribution, calculated theoretically using one of the available population analysis schemes, although arbitrary and method dependent, is a useful tool to study the electronic density distribution. The performed calculations indicate in most cases very little charge dispersion from the core ions to the ligand space. In the case of the N0 (H20>2 complex the calculated electron loss fi om NO amounts to 0.03 electron [66]. The similarity of the measured photoelectron spectra of NO and its complexes... 

Several attempts have been made to compute the atomic charge distributions (both ir-charges and total charges) and electric dipole moment216 0f oxazole, and thus to check the accuracies of the various MO procedures (see Table III). It is apparent from Table III that all-valence-electron calculations228 232 including the atomic polarization terms yield dipole moments very close to the experimental value.218 233... 

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